In ΔABC, D and E are points on the sides AB and AC, respectively, such that DE || BC. If AD = 5 cm, DB = 9 cm, AE = 4 cm and BC = 15.4 cm, then the sum of the lengths of DE and EC (in cm) is:

Each side of an equilateral triangle is 4 cm. What will be its area?

'G' is centroid of ΔABC if AG = BC then find ∠BGC.

In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?

A wire is in the shape of a rectangle. Its length is 42.7m and breadth is 21.8m. If the same wire is re-bent in the shape of a square, what will be the measure of the side of the square?

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

In ∆PQR, O is the incentre and ∠P = 42°. Then what is the measure of ∠QOR?